Gravity fields of the terrestrial planets

One of the important forces operating in the solar system is gravity, the force of mutual attraction between masses such as planets and satellites or the mutual attraction between small mass elements of a planet. Newton's law of gravitation, ‘two particles attract each other with a central force in proportion to the product of their masses and inversely in proportion to the square of the distance between them,’ has been found to be largely adequate to explain most gravitation phenomena in the solar system, whether it is orbital motions or the mass distributions within planets. The proportionality constant of Newton's law G, is 6.670 × 10−11 N m2 kg−2. An equivalent expression of Newton's law is in terms of the gravitational potential Φ, as the acceleration of gravity a, imparted by gravity on a test particle according to

(G19)

where ∇ is the gradient operator. For a body of volume V the potential at a point P outside of V is ...